Laravel eloquent ORM group where

Like this:

<?php

$results = DB::table('table')
             ->where(function($query) use ($starttime,$endtime){
                 $query->where('starttime', '<=', $starttime);
                 $query->where('endtime', '>=', $endtime);
             })
             ->orWhere(function($query) use ($otherStarttime,$otherEndtime){
                 $query->where('starttime', '<=', $otherStarttime);
                 $query->where('endtime', '>=', $otherEndtime);
             })
             ->orWhere(function($query) use ($anotherStarttime,$anotherEndtime){
                 $query->where('starttime', '>=', $anotherStarttime);
                 $query->where('endtime', '<=', $anotherEndtime);
             })
             ->get();

Have a look at the documentation for even more cool stuff you can do with Eloquent and the Query Builder.

//Edit:
To even wrap the whole where-clause in braces (like it is in your question), you can do this:

<?php

$results = DB::table('table')
             //this wraps the whole statement in ()
             ->where(function($query) use ($starttime,$endtime, $otherStarttime,$otherEndtime, $anotherStarttime,$anotherEndtime){

                 $query->where(function($query) use ($starttime,$endtime){
                     $query->where('starttime', '<=', $starttime);
                     $query->where('endtime', '>=', $endtime);
                 });

                 $query->orWhere(function($query) use ($otherStarttime,$otherEndtime){
                     $query->where('starttime', '<=', $otherStarttime);
                     $query->where('endtime', '>=', $otherEndtime);
                 });

                 $query->orWhere(function($query) use ($anotherStarttime,$anotherEndtime){
                     $query->where('starttime', '>=', $anotherStarttime);
                     $query->where('endtime', '<=', $anotherEndtime);
                 });
             })
             ->get();